Finite Group Databasebeta

← C2×#10589791 #11901890

Subgroups — C2×#10589791 #11901890

Order 1152.

1620 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#125C211yesmaximal, characteristic, complemented
2#10589791C2116yesmaximal, direct product factor
3C2×#63459C212yesmaximal
4C2×#63458C212yesmaximal
5C2×#63454C211yesmaximal, characteristic
6C2×C4⋊C4×D9C211yesmaximal, characteristic
7C2×#63452C211yesmaximal, characteristic, complemented
8C2×#63451C212yesmaximal, complemented
9C2×#63450C211yesmaximal, characteristic, complemented
10C2×#63450C212yesmaximal, complemented
11C2×#63434C211yesmaximal, characteristic
12C2×#63431C211yesmaximal, characteristic, complemented
13C2×#5689—31nomaximal
14C22×C4×D9C2212yes—
15C22×C4×D9C2211yescharacteristic
16C22×Dic18C2212yes—
17C22×Dic18C2212yes—
18C9×#125C2218yescomplemented
19C2×C9×C4⋊C4C2211yescharacteristic
20C2×C9×C4⋊C4C2212yes—
21C2×C9×C4⋊C4C2212yes—
22C2×C9×C4⋊C4C2211yescharacteristic
23C2×C42×C9C2211yescharacteristic
24C2×(C2×D9)⋊C4C2211yescharacteristic
25C2×(C2×D9)⋊C4C2211yescharacteristic
26C2×(C2×D9)⋊C4C2212yes—
27C2×C4⋊Dic9C2211yescharacteristic
28C2×C4⋊Dic9C2212yes—
29C2×C4⋊Dic9C2211yescharacteristic
30C2×C4⋊Dic9C2212yes—
31C2×Dic9⋊C4C2211yescharacteristic
32C2×Dic9⋊C4C2211yescharacteristic
33C2×Dic9⋊C4C2212yes—
34C2×Dic9⋊C4C2212yes—
35C2×Dic9⋊C4C2212yes—
36C2×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2212yes—
38#63459C22116yes—
39#63458C22116yes—
40#63454C2218yes—
41C4⋊C4×D9C2218yes—
42#63452C2218yescomplemented
43#63451C22116yescomplemented
44#63450C2218yescomplemented
45#63450C22116yescomplemented
46#63434C2218yes—
47#63431C2218yescomplemented
48C2×C3×#125D311yescharacteristic
49#5689—316no—
50C2×#897—32no—
51C2×#896—32no—
52C2×#892—31no—
53C2×D3×C4⋊C4—31no—
54C2×#890—31no—
55C2×#889—32no—
56C2×#888—31no—
57C2×#888—32no—
58C2×#872—31no—
59C2×#869—31no—
60C23×D9C2311yescharacteristic
61C22×C4×C9C2311yescharacteristic
62C22×C4×C9C2311yescharacteristic
63C22×C4×C9C2312yes—
64C22×C4×C9C2312yes—
65C22×C4×C9C2311yescharacteristic
66C22×Dic9C2311yescharacteristic
67C22×Dic9C2312yes—
68C22×Dic9C2311yescharacteristic
69C22×Dic9C2312yes—
70C22×Dic9C2311yescharacteristic
71C2×C4×D9—44no—
72C2×C4×D9Q818yescomplemented
73C2×C4×D9C2318yes—
74C2×C4×D9C2314yes—
75C2×Dic18—44no—
76C2×Dic18—44no—
77C2×Dic18C2318yes—
78C2×Dic18C2318yes—
79C9×C4⋊C4C2314yes—
80C9×C4⋊C4C2318yes—
81C9×C4⋊C4C2318yes—
82C9×C4⋊C4C2314yes—
83C42×C9C2314yes—
84(C2×D9)⋊C4C2314yes—
85(C2×D9)⋊C4C2314yes—
86(C2×D9)⋊C4C2318yes—
87C4⋊Dic9C2314yes—
88C4⋊Dic9C2318yes—
89C4⋊Dic9C2314yes—
90C4⋊Dic9C2318yes—
91Dic9⋊C4C2314yes—
92Dic9⋊C4C2314yes—
93Dic9⋊C4C2318yes—
94Dic9⋊C4C2318yes—
95Dic9⋊C4C2318yes—
96C4×Dic9C2314yes—
97C4×Dic9C2318yes—
98C2×#544—91noSylow
99C22×C4×D3—31no—
100C22×C4×D3—32no—
101C22×Dic6—32no—
102C22×Dic6—32no—
103C3×#125C2×D318yes—
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C4⋊C4C2×D312yes—
106C2×C3×C4⋊C4C2×D312yes—
107C2×C3×C4⋊C4C2×D311yescharacteristic
108C2×C3×C42C2×D311yescharacteristic
109C2×(C2×D3)⋊C4—31no—
110C2×(C2×D3)⋊C4—31no—
111C2×(C2×D3)⋊C4—32no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—32no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—32no—
116C2×Dic3⋊C4—31no—
117C2×Dic3⋊C4—31no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—32no—
121C2×C4×Dic3—31no—
122C2×C4×Dic3—32no—
123#897—316no—
124#896—316no—
125#892—38no—
126D3×C4⋊C4—38no—
127#890—38no—
128#889—316no—
129#888—38no—
130#888—316no—
131#872—38no—
132#869—38no—
133C23×C9C2411yescharacteristic
134C22×D9—22no—
135C22×D9—22no—
136C22×D9C2×Q814yes—
137C22×D9C2412yes—
138C2×C4×C9—22no—
139C2×C4×C9—24no—
140C2×C4×C9—22no—
141C2×C4×C9—24no—
142C2×C4×C9C2×Q814yes—
143C2×C4×C9C2414yes—
144C2×C4×C9C2414yes—
145C2×C4×C9C2412yes—
146C2×C4×C9C2412yes—
147C2×C4×C9C2412yes—
148C2×Dic9—22no—
149C2×Dic9—24no—
150C2×Dic9—24no—
151C2×Dic9—22no—
152C2×Dic9C2×Q814yes—
153C2×Dic9C2412yes—
154C2×Dic9C2412yes—
155C2×Dic9C2414yes—
156C2×Dic9C2414yes—
157C2×Dic9C2412yes—
158C4×D9—48no—
159C4×D9C2×Q8116yescomplemented
160Dic18—48no—
161Dic18—48no—
162#544—916no—
163C2×C4⋊Q8—92no—
164C2×C4⋊Q8—91no—
165C2×C4⋊Q8—91no—
166C2×#125—92no—
167C2×#125—91no—
168C2×#125D911yescharacteristic, complemented
169C2×C22⋊Q8—92no—
170C2×C22⋊Q8—92no—
171C2×#117—91no—
172C2×#117—91no—
173C22×C4⋊C4—91no—
174C23×D3—31no—
175C22×C3×C4C22×D312yes—
176C22×C3×C4C22×D312yes—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C22×C3×C4C22×D311yescharacteristic
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—32no—
184C22×Dic3—32no—
185C2×C4×D3—38no—
186C2×C4×D3—34no—
187C2×C4×D3—38no—
188C2×C4×D3—124no—
189C2×Dic6—38no—
190C2×Dic6—38no—
191C2×Dic6—124no—
192C2×Dic6—124no—
193C3×C4⋊C4C22×D314yes—
194C3×C4⋊C4C22×D318yes—
195C3×C4⋊C4C22×D318yes—
196C3×C4⋊C4C22×D314yes—
197C3×C42C22×D314yes—
198(C2×D3)⋊C4—34no—
199(C2×D3)⋊C4—34no—
200(C2×D3)⋊C4—38no—
201C4⋊Dic3—34no—
202C4⋊Dic3—38no—
203C4⋊Dic3—34no—
204C4⋊Dic3—38no—
205Dic3⋊C4—34no—
206Dic3⋊C4—34no—
207Dic3⋊C4—38no—
208Dic3⋊C4—38no—
209Dic3⋊C4—38no—
210C4×Dic3—34no—
211C4×Dic3—38no—
212C22×C9C22×Q812yes—
213C22×C9H(5,𝔽2)12yes—
214C22×C92−1+412yes—
215C22×C9C2511yescharacteristic
216C2×D9—28no—
217C2×D9—22no—
218C2×D9—22no—
219C2×D9C22×Q814yes—
220C4×C9—22no—
221C4×C9—24no—
222C4×C9—24no—
223C4×C9—22no—
224C4×C9C22×Q814yes—
225Dic9—22no—
226Dic9—24no—
227Dic9—24no—
228Dic9—22no—
229Dic9C22×Q814yes—
230C22×Q8—92no—
231C22×Q8—92no—
232C23×C4—91no—
233C23×C4—92no—
234C4⋊Q8—916no—
235C4⋊Q8—98no—
236C4⋊Q8—98no—
237#125—916no—
238#125—98no—
239#125C2×D918yescomplemented
240C22⋊Q8—916no—
241C22⋊Q8—916no—
242#117—98no—
243#117—98no—
244C2×C4⋊C4—92no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—91no—
247C2×C4⋊C4—91no—
248C2×C4⋊C4—91no—
249C2×C4⋊C4—92no—
250C2×C4⋊C4—92no—
251C2×C4⋊C4—92no—
252C2×C4⋊C4—92no—
253C2×C4⋊C4—98no—
254C2×C4⋊C4C2×D911yescharacteristic
255C2×C4⋊C4C2×D911yescharacteristic
256C2×C4⋊C4C2×D912yes—
257C2×C4⋊C4C2×D912yes—
258C2×C22⋊C4—91no—
259C2×C22⋊C4—92no—
260C2×C22⋊C4—91no—
261C2×C42—92no—
262C2×C42—91no—
263C2×C42C2×D911yescharacteristic
264C23×C3C23×D311yescharacteristic
265C22×D3—34no—
266C22×D3—32no—
267C22×D3—62no—
268C22×D3—62no—
269C2×C3×C4—22no—
270C2×C3×C4—24no—
271C2×C3×C4—24no—
272C2×C3×C4—22no—
273C2×C3×C4D3×Q814yes—
274C2×C3×C4C23×D314yes—
275C2×C3×C4C23×D314yes—
276C2×C3×C4C23×D312yes—
277C2×C3×C4C23×D312yes—
278C2×C3×C4C23×D312yes—
279C2×Dic3—34no—
280C2×Dic3—32no—
281C2×Dic3—32no—
282C2×Dic3—32no—
283C2×Dic3—34no—
284C2×Dic3—34no—
285C2×Dic3—62no—
286C2×Dic3—64no—
287C2×Dic3—64no—
288C2×Dic3—62no—
289C4×D3—316no—
290C4×D3—128no—
291Dic6—128no—
292Dic6—128no—
293C2×C9#54414yescomplemented
294C2×C9C23×Q811yescharacteristic
295C2×C9C2×H(5,𝔽2)11yescharacteristic
296C2×C9C2×2−1+411yescharacteristic
297D9—24no—
298C24—91no—
299C2×Q8—98no—
300C2×Q8—98no—
301C2×Q8—364no—
302C2×Q8—364no—
303C22×C4—91no—
304C22×C4—98no—
305C22×C4—94no—
306C22×C4—91no—
307C22×C4—91no—
308C22×C4—92no—
309C22×C4—92no—
310C22×C4—98no—
311C22×C4—364no—
312C22×C4C22×D912yes—
313C22×C4C22×D911yescharacteristic
314C22×C4C22×D911yescharacteristic
315C22×C4C22×D912yes—
316C22×C4C22×D911yescharacteristic
317C4⋊C4—98no—
318C4⋊C4—94no—
319C4⋊C4—94no—
320C4⋊C4—94no—
321C4⋊C4—94no—
322C4⋊C4—98no—
323C4⋊C4—98no—
324C4⋊C4—98no—
325C4⋊C4—98no—
326C4⋊C4C22×D914yes—
327C4⋊C4C22×D914yes—
328C4⋊C4C22×D918yes—
329C4⋊C4C22×D918yes—
330C22⋊C4—94no—
331C22⋊C4—98no—
332C22⋊C4—94no—
333C42—98no—
334C42—94no—
335C42C22×D914yes—
336C22×C3C2×D3×Q812yes—
337C22×C3#100912yes—
338C22×C3#101012yes—
339C22×C3C24×D311yescharacteristic
340C2×D3—34no—
341C2×D3—68no—
342C2×D3—62no—
343C2×D3—62no—
344C3×C4—22no—
345C3×C4—24no—
346C3×C4—24no—
347C3×C4—22no—
348C3×C4C2×D3×Q814yes—
349Dic3—34no—
350Dic3—62no—
351Dic3—64no—
352Dic3—64no—
353Dic3—62no—
354C9C2×#54411yescharacteristic, complemented, Sylow
355C23—92no—
356C23—94no—
357C23—182no—
358C23—182no—
359C23C23×D911yescharacteristic
360Q8—368no—
361Q8—368no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—24no—
365C2×C4—22no—
366C2×C4—92no—
367C2×C4—94no—
368C2×C4—916no—
369C2×C4—92no—
370C2×C4—92no—
371C2×C4—94no—
372C2×C4—94no—
373C2×C4—184no—
374C2×C4—182no—
375C2×C4—184no—
376C2×C4—182no—
377C2×C4—368no—
378C2×C4Q8×D914yes—
379C2×C4C23×D914yes—
380C2×C4C23×D912yes—
381C2×C4C23×D912yes—
382C2×C4C23×D914yes—
383C2×C4C23×D912yes—
384C2×C3#568914yes—
385C2×C3C22×D3×Q811yescharacteristic
386C2×C3C2×#100911yescharacteristic
387C2×C3C2×#101011yescharacteristic
388D3—64no—
389C22—94no—
390C22—188no—
391C22—182no—
392C22—182no—
393C22C2×Q8×D912yes—
394C22#6371512yes—
395C22#6371612yes—
396C22C24×D911yescharacteristic
397C4—24no—
398C4—22no—
399C4—24no—
400C4—22no—
401C4—94no—
402C4—184no—
403C4—182no—
404C4—184no—
405C4—182no—
406C4C2×Q8×D914yes—
407C3C2×#568911yescharacteristic
408C2—184no—
409C2#1058979114yesdirect product factor
410C2C22×Q8×D911yescharacteristic
411C2C2×#6371511yescharacteristic
412C2C2×#6371611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C9×#125C2
socleC23×C3C23×D3
prime radicalC23×D9C23
hypercenterC2×#125D9
hypocenterC9C2×#544
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C9×#125C2semidirect
2. #10589791C2direct (N × H)
7. C2×#63452C2semidirect
8. C2×#63451C2semidirect
9. C2×#63450C2semidirect
10. C2×#63450C2semidirect
12. C2×#63431C2semidirect
18. C9×#125C22semidirect
42. #63452C22semidirect
43. #63451C22semidirect
44. #63450C22semidirect
45. #63450C22semidirect
47. #63431C22semidirect
72. C2×C4×D9Q8semidirect
159. C4×D9C2×Q8semidirect
168. C2×#125D9semidirect
239. #125C2×D9semidirect
293. C2×C9#544semidirect
354. C9C2×#544semidirect
409. C2#10589791direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C9×#1252
#105897912
C2×#634592
C2×#634582
C2×#634542
C2×C4⋊C4×D92
C2×#634522
C2×#634512
C2×#634502
C2×#634342
C2×#634312
C2×#56893